Interpreting Uncertainty in Discrete Time

The interpretation of a ultidyn element as a continuous-time or discrete-time system depends on the nature of the uncertain system (uss) within which it is an uncertain element.

For example, create a scalar ultidyn object. Then, create two 1-input, 1-output uss objects using the ultidyn object as their "D" matrix. In one case, create without specifying sample-time, which indicates continuous time. In the second case, force discrete-time, with a sample time of 0.42.

delta = ultidyn('delta',[1 1]); 
sys1 = uss([],[],[],delta) 
USS: 0 States, 1 Output, 1 Input, Continuous System 
  delta: 1x1 LTI, max. gain = 1, 1 occurrence 
sys2 = uss([],[],[],delta,0.42) 
USS: 0 States, 1 Output, 1 Input, Discrete System, Ts = 0.42 
  delta: 1x1 LTI, max. gain = 1, 1 occurrence 

Next, get a random sample of each system. When obtaining random samples using usample, the values of the elements used in the sample are returned in the 2nd argument from usample as a structure.

[sys1s,d1v] = usample(sys1); 
[sys2s,d2v] = usample(sys2); 

Look at d1v.delta.Ts and d2v.delta.Ts. In the first case, since sys1 is continuous-time, the system d1v.delta is continuous-time. In the second case, since sys2 is discrete-time, with sample time 0.42, the system d2v.delta is discrete-time, with sample time 0.42.

d1v.delta.Ts 
ans = 
     0 
d2v.delta.Ts 
ans = 
    0.4200 

Finally, in the case of a discrete-time uss object, it is not the case that ultidyn objects are interpreted as continuous-time uncertainty in feedback with sampled-data systems. This very interesting hybrid theory is beyond the scope of the toolbox.

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